How does momentum/'forward' thrust affect an object inside a vehicle in space? Apologies if this is a worn-out question, but I'm curious about this: if you're inside a vehicle in space, and that vehicle begins to move in a direction under its own power, would you 'drift' towards the origin of the thrust of the vehicle?
Put another way, if you have thrusters on the 'floor' side of a ship, would using those thrusters create a form of gravity, in that you would be pulled towards the floor while the thrusters were active?
 A: The acceleration caused by the thrusters would produce the effect of gravity pulling you towards the floor, and in fact, you wouldn't be able to tell the difference from "real gravity" as the inside occupant.  You can read more here:  https://en.wikipedia.org/wiki/Equivalence_principle
I hope this helps.
A: Using those thrusters would not create a form of gravity, but would create an effect of artificial gravity. 
Infact, if the spaceship had no windows, perfect sound insulation, and moved at an acceleration equal to that caused by gravity on the surface of the Earth you would not even be able to tell the difference between this case and the case of your spaceship being stationary on the surface of the Earth.
To understand this you can think of it like this; here on the surface of the Earth we move towards the Earth at an acceleration of about $9.8 ms^{-2}$ and the Earth remains stationary (for the most part! look at the note). In the case of you on the spaceship, you remain stationary and the spaceship moves towards you at an acceleration of $9.8 ms^{-2}$, since the relative accelerations are the same in both the cases we cannot tell the difference.
Slightly off topic, but as einstein had once explained you would also not be able to tell the difference between being in a spaceship in free fall and one in space which is not accelerating. This follows according to the same principle mentioned above.
note: Actually, not only are we accelerating towards the Earth but the Earth is also accelerating towards us, although at an extremely tiny acceleration. If we add up both these accelerations we get $9.8ms^{-2}$, which is basically the relative acceleration. This is because of the concept of centre of mass. Since this question does not discuss that I will not elaborate further...but you can check this link out:click here
Hope this helps!
